In the first essay, "Do Firms Knowingly Sell Overvalued Equity?", I develop a simple equilibrium model which shows that insider trading around seasoned equity offerings (SEO) depends on both the quality of issuing firms and insiders' exogenous consumption shocks, neither of which are known by outside investors in the model. The empirical evidence indicates that insider trading is not reliably related to the future long-term stock returns of issuing firms even though it is reliably related to their announcement period abnormal returns. Issuing firms underperform their benchmarks regardless of the prior insider trading pattern. This suggests that insiders who have purchased shares before issuing do not realize that the market has overcapitalized prior good news, and are not knowingly selling overvalued equity.The second essay, "Deposit Insurance with Changing Volatility: An Application of Exotic Options", develops a model to incorporate the bank managers' incentives to change the bank's volatility into the pricing of deposit insurance. It is assumed that the volatility of the bank's assets changes or can be changed when the assets first hit a certain level. The results show that the shareholders' equity and the deposit insurance premium can be represented as combinations of generalized versions of particular barrier options known as down-and-out and down-and-in options. Numerical examples are used to illustrate the properties of the model.